This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A171117 #12 Apr 28 2024 06:27:12
%S A171117 1,0,1,4,105,2576,122129,7397760,629336977,68265049600,9386419113537,
%T A171117 1583207240397824,322519291535862713,77985053716765181952,
%U A171117 22094670475785827572945,7249172440569540585914368,2727206213196927179246863137,1166222035906526210266584842240
%N A171117 A particular case of Gromov-Witten numbers: a(n) is the number of complex rational curves of degree n and genus 0 in CP^3 passing through 2n given points.
%H A171117 Erwan Brugallé and Grigory Mikhalkin, <a href="https://doi.org/10.1016/j.crma.2007.07.026">Enumeration of curves via floor diagrams</a>, C. R. Acad. Sci. Paris, Ser. I, 345 (2007), 329-334; arXiv:<a href="https://arxiv.org/abs/0706.0083">0706.0083</a> [math.AG], 2007.
%H A171117 Penka Georgieva and Aleksey Zinger, <a href="https://doi.org/10.1215/00127094-2017-0023">Enumeration of real curves in CP^{2n-1} and a Witten-Dijkgraaf-Verlinde-Verlinde relation for real Gromov-Witten invariants</a>, Duke Math. J., 166 (2017), 3291-3347; arXiv:<a href="https://arxiv.org/abs/1309.4079">1309.4079</a> [math.SG], 2013-2017. See Eq. (7.1).
%F A171117 a(n) ~ c * d^n * n^(2*n-3), where d = 0.22437689379499207235291475487670864472074175469311760751181993..., c = 2.114876309952735589169436238081913983666848627651832555153... - _Vaclav Kotesovec_, Apr 28 2024
%t A171117 n[1] = nt[1] = 1;
%t A171117 n[d_] := n[d] = Sum[With[{d2 = d - d1}, (d2^2 Binomial[2 d - 3, 2 d1 - 2] - d1 d2 Binomial[2 d - 3, 2 d1 - 1]) nt[d1] n[d2]], {d1, d - 1}];
%t A171117 nt[d_] := nt[d] = d n[d] + Sum[With[{d2 = d - d1}, (d1 d2^2 Binomial[2 d - 2, 2 d1 - 1] - d2^3 Binomial[2 d - 2, 2 d1 - 2]) nt[d1] n[d2]], {d1, d - 1}];
%t A171117 Table[n[d], {d, 20}] (* _Andrey Zabolotskiy_, May 03 2022 *)
%Y A171117 Cf. A013587.
%K A171117 nonn
%O A171117 1,4
%A A171117 _N. J. A. Sloane_, Sep 27 2010
%E A171117 Name edited, terms a(8) and beyond added by _Andrey Zabolotskiy_, May 03 2022